Gas Flow Through Square Arrays of Circular Cylinders with Klinkenberg Effect: A Lattice Boltzmann Study (Communications in Computational Physics, 2010)
It is well known that, as non-continuum gas flows through microscale porousmedia, the gas permeability derived from Darcy law is larger than the absolute permeability,which is caused by the so-called Klinkenberg effect or slippage effect. In thispaper, an effective definition of Knudsen number for gas flows through square arraysof circular cylinders and a local boundary condition for non-continuum gas flows arefirst proposed, and then the multi-relaxation-time lattice Boltzmann equation includingdiscrete effects on boundary condition is used to investigate Klinkenberg effect ongas flow through circular cylinders in square arrays. Numerical results show that thecelebrated Klinkenberg equation is only correct for low Knudsen number, and second-ordercorrection to Klinkenberg equation is necessary with the increase of Knudsennumber. Finally, the present numerical results are also compared to some availableresults, and in general an agreement between them is observed.